where \(m_{1,2}\)  are the mass of the two test objects, \(G\)  is the Newton's constant and \(u\simeq 0.931\,\) GeV is the atomic mass unit.
The quantity \(\alpha _G\equiv ({g^{\prime 2} Z^2})/({G A^2 u^2})\)  is bounded from above as a function of the interaction range \(\lambda \equiv 1/M_{Z^{\prime }}\)  [1]}, [2]}.
To translate the bound into that for \(g^{\prime }\)  we make an approximation that for most materials \(Z/A\simeq 0.5\) .
The current limit on \(g^{\prime }\)  is shown by the orange shaded region (excluded) in Fig. REF .
